Magnetoresistive device

ABSTRACT

A method of operating a magnetoresistive device is described. The device comprises a ferromagnetic region configured to exhibit magnetic anisotropy and to allow magnetisation thereof to be switched between at least first and second orientations and a gate capacitively coupled to the ferromagnetic region. The method comprises applying an electric field pulse to the ferromagnetic region so as to cause orientation of magnetic anisotropy to change for switching magnetisation between the first and second orientations.

FIELD OF THE INVENTION

The present invention relates to a magnetoresistive device.

BACKGROUND ART

Magnetic random access memory (MRAM) has several advantages over othertypes of non-volatile memory, such as Flash memory. For example, MRAMusually consumes less power and is faster to read and write data. MRAMalso offers a promising alternative to some forms of volatile memory,such as dynamic random access memory (DRAM).

A conventional MRAM cell typically includes a magnetoresistive elementwhich has a pair of ferromagnetic layers separated by a non-magneticlayer. One of the ferromagnetic layers has a relatively low coercivityand the other has a relatively high coercivity. The low- andhigh-coercivity layers are usually referred to as “free” and “pinned”layers respectively.

To store data in the cell, an external magnetic field is applied whichorientates the magnetisation of the free layer. After the magnetic fieldis removed, the orientation of the magnetisation is retained.

To read data from the cell, a current is driven through the element. Themagnetoresistance of the element is relatively high if themagnetisations of the layers are arranged in anti-parallel (AP) and isrelatively low if the magnetisations of the layers are arranged inparallel (P). Thus, the state of the cell can be determined by measuringthe magnetoresistance of the element.

The external magnetic field is generated by passing a current through atleast one conductive line running close to the element. However, thisarrangement suffers the problem that as the size of the cell decreases,the magnetic field required to switch the free layer increases and sopower consumption also increases.

An alternative to applying an external magnetic field is to employ spintransfer switching, as proposed in “Current-driven Excitation ofMagnetic Multilayers” by J. C. Slonczewski, p. 9353, Phys. Rev. B, Vol.54 (1996), and reference is made to “Highly scalable MRAM using fieldassisted current induced switching” by W. C. Jeong et al., p. 184, 2005Symposium on VLSI Technology Digest of Technical Papers.

In spin transfer switching, a current is driven through the magneticelement perpendicular to the layer interfaces. This causesspin-polarised electrons to be injected into the free layer either byelectrons flowing through the pinned layer (when current is driven fromthe free layer to the pinned layer) or by electrons scattering from thepinned layer (when current is driven from the pinned layer to the freelayer). When spin polarised electrons are injected into the free layer,they interact with the free layer and transfer a portion of their spinangular momentum to the magnetic moment of the free layer. If thespin-polarised current is sufficiently large, then this can cause themagnetisation of the free layer to switch.

A drawback, however, of spin transfer switching is that a high currentdensity (e.g. of the order of 10⁸ Acm⁻²) is needed to trigger thereversal process.

The current may be reduced by applying a dc pre-charging current beforeapplying a switching current pulse, as described in “Prechargingstrategy to accelerate spin-transfer switching below the nanosecond” byT. Devolder et al., Applied Physics Letters, volume 86, page 062505(2005). Although the power consumption of the switching current pulse isreduced, the overall power consumption (i.e. including the powerconsumption of the pre-charging current) is still quite large.

However, the current may be reduced by applying a short (e.g. <5 ns)external magnetic field pulse along a magnetic hard axis of the freelayer immediately prior to or simultaneously with applying a switchingcurrent pulse so as to cause precessional switching, as described in“Micromagnetic simulation of spin transfer torque switching combinedwith precessional motion from a hard axis magnetic field” by K. Ito etal., Applied Physics Letters, volume 89, page 252509 (2006).

Although this technique can reduce the spin transfer currentsignificantly, it involves applying an external magnetic field bypassing a current through a line. This limits the potential forscalability and reducing power consumption.

The present invention seeks to ameliorate this problem.

SUMMARY OF THE INVENTION

According to a first aspect of the present invention there is provided amethod of operating a magnetoresistive device comprising a ferromagneticregion configured to exhibit magnetic anisotropy and to allowmagnetisation thereof to be switched between at least first and secondorientations and a gate capacitively coupled to the ferromagneticregion, the method comprising applying an electric field pulse to theferromagnetic region so as to cause orientation of magnetic anisotropyto change for switching magnetisation between the first and secondorientations. Thus, precession-assisted magnetisation switching can betriggered using less power than a device having a conductive line forgenerating a magnetic field pulse.

The method may comprise exclusively applying the electric field pulse tothe ferromagnetic region so as to cause magnetisation of theferromagnetic region to switch between the first and secondorientations. The method may comprise arranging for magnetisation of theferromagnetic region to switch between the first and second orientationswithout applying a magnetic field pulse. Using only an electric fieldpulse to cause magnetisation of the ferromagnetic region to switchbetween the first and second orientations or not using a magnetic fieldpulse to assist switching helps to minimise power consumption.

The device may further comprise a conductive path running adjacent tothe ferromagnetic region for generating a magnetic field pulse, themethod further comprising applying a magnetic field pulse to theferromagnetic region while applying the electric field pulse so toenhance the change orientation of effective magnetic field whichcomprises the anisotropy field during the electric field pulse and theapplied magnetic field pulse so as to switch the magnetisation betweenthe first and second orientations. The method may comprise applying aleading edge of the electric field pulse before applying a leading edgeof the magnetic field pulse.

The device may further comprise another ferromagnetic region having ahigher coercivity than the ferromagnetic layer and separated therefromby a tunnel barrier layer, the method further comprising applying a spintransfer current pulse passing through ferromagnetic regions whileapplying the electric field pulse so as to switch the magnetisationbetween the first and second orientations.

The method may further comprise applying a leading edge of the electricfield pulse before applying a leading edge of the spin transfer currentpulse. The ferromagnetic region may comprises a ferromagneticsemiconductor having an inhomogeneous strain distribution and the methodcomprises applying an electric field pulse of sufficient magnitude tovary distribution of charge carriers relative to the inhomogeneousstrain distribution.

The inhomogeneous strain distribution comprises a region of compressivestrain and a region of tensile strain. The ferromagnetic semiconductormay comprise (Ga,Mn)As.

The method may comprise applying an electric field pulse having aduration, t, which is a multiple of a quarter of t_(precess) about:

$t_{precess} = {{1/f_{precess}} = \frac{1}{\frac{\gamma}{2\pi}B_{A}}}$

where γ is the gyromagnetic constant γ=gμ_(B)/

(2.2×10¹⁵ mA⁻¹s⁻¹) and B_(A) is the magnetic anisotropy field of theferromagnetic semiconductor. The method may comprise applying a pulsehaving a duration, t, between 0 and 5 ns.

The method may further comprise applying a magnetic field to theferromagnetic region independently of applying the electric field pulseso as to assist switching of the magnetisation of the ferromagneticregion between the first and second orientations.

The method may comprise applying stress to the ferromagnetic region and,while the stress is applied, applying the electric field pulse.

According to a second aspect of the present invention there is provideda method of operating a magnetoresistive device comprising aferromagnetic region configured to exhibit magnetic anisotropy and toallow magnetisation thereof to be switched between at least first andsecond orientations, the method comprising applying a stress pulse tothe ferromagnetic region so as to cause orientation of magneticanisotropy to change for switching magnetisation between the first andsecond orientations. Thus, precessional or precesion-assistedmagnetisation switching can be triggered using less power than a devicehaving a conductive line for generating a magnetic field pulse.

The device may comprise a piezoelectric region mechanically coupled tothe ferromagnetic region and wherein applying the stress pulse comprisesapplying a voltage pulse across the piezoelectric region.

The method may comprise applying an electric field pulse to theferromagnetic region while the stress pulse is applied to theferromagnetic region.

According to third aspect of the present invention there is providedapparatus comprising a magnetoresistance device comprising aferromagnetic region configured to exhibit magnetic anisotropy and toallow magnetisation thereof to be switched between at least first andsecond orientations and circuitry configured to operate the deviceaccording to the method.

According to a fourth aspect of the present invention there is provideda magnetoresistive device comprising a ferromagnetic region configuredto exhibit magnetic anisotropy and to allow magnetisation thereof to beswitched between at least first and second orientations, means forapplying stress to the ferromagnetic region in response to a firstelectrical input and means for applying an electric field to theferromagnetic region in response to a second electrical input.

The means for applying stress may comprise a piezoelectric regioncoupled to the ferromagnetic region and the means for applying anelectric field may comprise at least one gate electrode.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will now be described, by way ofexample, with reference to the accompanying drawings in which:

FIG. 1 illustrates applying an electric field pulse to a ferromagneticelement to cause a change in orientation of magnetic anisotropy and toswitch magnetisation in accordance with the present invention;

FIG. 2 a is a scanning electron micrograph of a device in whichorientation of magnetic anisotropy varies due tolithographically-induced strain relaxation and of a van der Pauw devicewithout strain variation;

FIG. 2 b is a magnified view of the device shown in FIG. 2 a;

FIG. 2 c is a cross-section of a layer structure from which the deviceand the van der Pauw device shown in FIG. 2 a are fabricated;

FIG. 3 a shows of plots of longitudinal anisotropic magnetoresistance at4.2° K for [1 10]- and [110]-orientated arms of the device shown in FIG.2 a in a rotating magnetic field having a fixed magnetic field magnitude(B=4T) with angles measured from the [110]-axis;

FIG. 3 b shows plots of transverse magnetoresistance at 4.2° K for [110] and [110] arms for the device shown in FIG. 2 a and also for the vander Pauw device shown in FIG. 2 a in a rotating magnetic field having afixed magnetic field magnitude (B=4T) with angles measured from the[110] axis;

FIG. 3 c shows plots of longitudinal anisotropic magnetoresistance at4.2° K for [110] orientated arm of a device similar to that shown inFIG. 2 a but having a wider and longer channel in a varying magneticfield in at different angle;

FIG. 3 d shows plots of longitudinal anisotropic magnetoresistance at4.2° K for [110] orientated arm of the device shown in FIG. 2 a in afixed-angle varying magnetic field;

FIG. 4 a shows plots of transverse resistance measurement at 4.2° K forthe van der Pauw device shown in FIG. 2 a;

FIG. 4 b shows plots of transverse resistance measurement at 4.2° K forthe device shown in FIG. 2 a;

FIG. 5 a shows a 2-dimensional plot of numerical simulated values ofstrain along an [001]-axis for a transverse cross section of the deviceshown in FIG. 2 a;

FIG. 5 b shows a plot of numerical simulated values of strain along an[110]-axis for a transverse cross section of the device shown in FIG. 2a;

FIG. 5 c shows a plot of simulated values of strain a different cutsthrough the [001]-plane for the device shown in FIG. 2 a;

FIG. 5 d shows a plot of simulated values of strain a different cutsthrough the [110]-plane for the device shown in FIG. 2 a;

FIG. 6 a illustrates easy axis orientations for [110] and [1 10]orientated arms of a device similar to that shown in FIG. 2 a and alsofor the device shown in FIG. 2 a;

FIG. 6 b shows plots of theoretical magnetocrystalline energy values asa function of in-plane magnetisation angle at different strains andalong different directions;

FIG. 7 illustrates a magnetocrystalline energy profile ofGa_(0.96)Mn_(0.04)As grown on [001]-orientated GaAs under compressivestrain for two different carrier concentrations;

FIGS. 8 a, 8 b and 8 c a schematic view of first, second and thirddevices in which orientation of magnetic anisotropy in a ferromagneticelement can be varied in accordance with the present invention;

FIG. 9 is a perspective view of the first device shown in FIG. 8 a;

FIG. 10 a is a plot of channel conductance against gate voltage andin-plane, parallel-to-current magnetic field for the device shown inFIG. 10 a;

FIG. 10 b shows Coulomb blockade oscillations for the device shown inFIG. 9;

FIG. 10 c shows a plot of critical reorientation magnetic field againstgate voltage for the device shown in FIG. 9;

FIG. 11 a is a plan view of the second device shown in FIG. 8 b;

FIG. 11 b is a cross-sectional view of the second device shown in FIG. 8b taken along the line A-A′;

FIG. 12 illustrates writing and read cycles for the devices shown inFIGS. 8 a and 8 b;

FIGS. 13 a, 13 b and 13 c illustrate fabrication of the first deviceshown in FIG. 8 a at different stages;

FIG. 14 a is a perspective view of the third device shown in FIG. 8 c;

FIG. 14 b is a cross-sectional view of the third device taken along theline B-B′;

FIG. 15 illustrates writing and read cycles for the device shown in FIG.8 c;

FIG. 16 a is a plan view of another device in which orientation ofmagnetic anisotropy in a ferromagnetic element can be varied inaccordance with the present invention;

FIG. 16 b is a longitudinal cross-sectional view of the device shown inFIG. 16 a taken along the line C-C′;

FIG. 16 c is a transverse cross-sectional view of the device shown inFIG. 16 a taken along the line D-D′;

FIG. 17 illustrates a layer structure used to fabricate the device shownin FIG. 15;

FIG. 18 is a transverse cross-sectional view of a modified version ofthe device shown in FIG. 16 a;

FIG. 19 schematically illustrates varying carrier distribution with aferromagnetic semiconductor;

FIG. 19 a illustrates re-orientation of magnetic anisotropy;

FIG. 20 a is a plan view of a fourth device in which orientation ofmagnetic anisotropy in a ferromagnetic element can be varied inaccordance with the present invention;

FIG. 20 b is a cross-sectional view of a the device shown in FIG. 20 ataken along the line E-E′;

FIG. 21 a is a plan view of a fifth device in which orientation ofmagnetic anisotropy in a ferromagnetic element can be varied inaccordance with the present invention;

FIG. 21 b is a cross-sectional view of a the device shown in FIG. 21 ataken along the line F-F′;

FIG. 22 illustrates writing and read cycles for the device shown in FIG.21 a;

FIG. 23 illustrates a ferromagnetic element having 6 remnantmagnetisation orientations;

FIG. 24 illustrates switching between the remnant magnetisationorientations shown in FIG. 23 in accordance with the present invention;and

FIGS. 25 a and 25 b illustrate applying electric field pulses to theferromagnetic element shown in FIG. 23 to cause a change in orientationof magnetic anisotropy and to switch magnetisation in accordance withthe present invention.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

Electric Field Pulse Induced Magnetization Reversal

Referring to FIG. 1, a ferromagnetic element 1 of a magnetoresistivedevice in accordance with the present invention is shown. Theferromagnetic element 1 is assumed to have homogenously distributedmagnetization, although this need not necessarily be the case.

The ferromagnetic element 1 is exhibits magnetic anisotropy defining amagnetic easy axis 2. Magnetic anisotropy may arise as a result of,inter alia, the shape of the element and/or crystal structure. Forexample, the element 1 may be elongate and so the magnetic easy axis 2may be aligned along a longitudinal axis.

Magnetisation 3 of the element 1 is aligned along a magnetic easy axis2.

An external magnetic field 5 may optionally be applied to supportprecessional switching and, depending on orientation, to stabilizere-orientation of the magnetisation 3. For example, the externalmagnetic field 5 may be applied globally to an array of ferromagneticelements (of which the ferromagnetic element 1 is one). The externalmagnetic field 5 may be fixed along the hard axis to facilitate orassist the precessional switching, for example using a permanent magnet.

As shown in FIG. 1, the external magnetic field 5 is alignedanti-parallel to the initial magnetization along the easy axis 2 tostabilize re-orientation of the magnetisation 3. However, the externalmagnetic field 5 need not be aligned along the easy axis 2 and may beorientated at other angles including a hard axis which, for thearrangement shown in FIG. 1, is arranged perpendicular to the easy axis2. The external magnetic field 5 may be variable and may be generated bypassing a current through a conductive track (not shown).

The magnetic anisotropy field and the optional external magnetic field 5result(s) in an effective magnetic field 6, namely:

{right arrow over (B)} _(eff) ={right arrow over (B)} _(A) +{right arrowover (B)} _(ext)   (1)

where {right arrow over (B)}_(eff) is the effective magnetic field 6acting on the magnetization 3, {right arrow over (B)}_(A) is theanisotropy field and {right arrow over (B)}_(ext) is the externalmagnetic field 5 (expressed in vector notation).

As will now be explained, an electric field pulse 7 may be applied, forexample perpendicularly to the plane of the layer, to change magneticanisotropy in the ferromagnetic element 1 temporarily and triggerprecessional reorientation of the magnetization 3.

Before the electric field pulse 7 is applied, in other words at t<0 andV=V₀ (e.g. V₀=0), where t is time and V is a bias applied to a gate (notshown), the magnetization 3 (shown as {right arrow over (M)}) isorientated in the direction of the effective magnetic field 6 (heredesignated as parallel to positive x-direction). In some embodiments,more than one gate (not shown) may be used.

An electric field pulse 7 is then applied, which causes magneticanisotropy to change and, thus, the magnetization 3 to be rotated and tobegin precessing around the modified effective field.

Therefore, at the beginning of the pulse 7, i.e. at t=0 and V=V_(C), theanisotropy field 2 changes causing the effective magnetic field 6 torotate, i.e. {right arrow over (B)}_(eff) ⁺(V₀)→{right arrow over(B)}_(eff)(V_(C)), and the magnetization 3 starts damped precessionaround the axis of effective magnetic field 6, i.e. around {right arrowover (B)}_(eff)(V_(C)).

Once the magnetisation 3 has carried out a half precession, the electricfield 7 can be switched off. The magnetisation 3 then begins tostabilize (anti-parallel) along the easy axis 2.

Therefore, at the end of the pulse 7, when t=Δt_(180°) and V=V_(C), theanisotropy field and the effective magnetic field 6 have acquired anegative x-component, as shown in FIG. 1 c.

Shortly after the pulse 7 has ended, when t=Δt_(180°)+δ (where δ>0) andV_(G)=V₀, the anisotropy field 2 has reversed and is alignedanti-parallel to its original orientation, i.e. {right arrow over(B)}_(eff)(V_(C))→{right arrow over (B)}_(eff) ⁻(V₀), parallel−x-direction and the magnetisation 3 continues damped precession aroundthe axis of effective magnetic field 6, i.e. around {right arrow over(B)}_(eff)(V₀).

When t>>Δt_(180°) and V_(G)=V₀, the magnetisation 3 reaches equilibriumand is aligned along the effective magnetic field, which is parallel(−x)-direction, i.e. {right arrow over (B)}_(eff) ⁻(V₀).

Magnetisation reversal may be understood by consideringorientation-dependent energy of magnetization 3. For example, for V₀,the easy axis 2 along the x-axis corresponds to two energy minimadivided by a potential barrier. The height of the barrier corresponds tothe energy increase if the magnetization 3 is aligned along the hardaxis.

Magnetization reversal, i.e. reorientation of magnetization by 180°, canbe used in a tunnelling magnetoresistance (TMR) device, giganticmagnetoresistance (GMR) device and other similar types of read devicewhere the relative orientation between the switched layer and a fixedreference layer determine the resistance of the device.

If the gate voltage pulse 7 results in a new easy axis which is rotatedfrom the original easy axis 4 by more than 45° and up to 90°, thenmagnetization reversal can be achieved without using an assist magneticfield.

This can be achieved in Ga_(1-x)Mn_(x)As at high carrier density, forexample when x>0.03, for example, by spatially varying strain within theelement 1 from a location in which it is in tensile strain, in whichanisotropy is orientated perpendicular to the plane of the layer, to alocation in which it is in compressive strain, in which magneticanisotropy is orientated in the plane of the layer. Rotation of easyaxis can also be achieved by changing the carrier density in a strainedconfiguration.

In low doped Ga_(1-x)Mn_(x)As, where x<0.02, magnetic anisotropyvariation can behave in an opposite way. For example, in a location inwhich the element is compressively strained, magnetic anisotropy may beorientated perpendicularly to the plane and in a location in which theelement is in tensile strain, the magnetic anisotropy is orientated inplane

Depending on the particular magnetic anisotropy of the system, acomplete magnetisation reversal is not necessary, in other wordsmagnetisation need not be re-orientated by 180°. For example,magnetization reorientation of 90° can be achieved in an elementexhibiting cubic magnetic anisotropy, if the easy axis rotates by anangle less than or equal to 22.5° with a longer pulse length (e.g. ahalf precession pulse) or at larger angles up to 90° for a shorter pulselengths (e.g. a quarter precession pulse). This can occur in such as wehave observed in Ga_(1-x)Mn_(x)As having very small strain variationsresulting from changes in lattice constant of the order of ˜0.01%. Inthis case, also anisotropic magnetoresistance effects, such asanisotropic magnetoresistance (AMR), tunnelling anisotropicmagnetoresistance (TAMR) or Coulomb blockade anisotropicmagnetoresistance (CBAMR) can be used to read out the magnetizationorientation.

Local Control of Magnetocrystalline Anisotropy in (Ga,Mn)As Devices

FIGS. 2 a and 2 b illustrate a device 8 in which magnetocrystallineanisotropies are tuned and controlled using strain relaxation arisingfrom lithographically-defined trenches 9. The magnetocrystallineanisotropies are induced by spin-orbit coupling. To aid characterisationof magnetic anisotropy of both bulk GaMnAs and the effect of strainrelaxation in the device 8, a van der Pauw device 10 is defined in thewafer 11 adjacent to the device 8.

The device 8 is in the form of a Hall bar having a channel 11 which is‘L’-shaped in plan view and which includes first and second arms 11 ₁,11 ₂ orthogonally aligned along the [110] and [1 10] directions. Thearms have a (transverse) width, w, of 1 μm and a (longitudinal) length,l, of 20 μm.

Referring in particular to FIG. 2 c, the device 8 is formed in a waferhaving a layer structure 12 comprising a Ga_(0.95)Mn_(0.05)Asepitaxially-grown layer 13 (or “epilayer) having a thickness of 25 nmgrown along the [001] crystal axis on a GaAs substrate 14. The channel11 is defined using electron beam lithography and reactive ion-beametching. The trenches 9 have a (transverse) width, W, of 200 nm and adepth, d, of 70 nm.

Referring to FIGS. 3 a to 3 d, electrical characteristics for anotherdevice (not shown) having an identical configuration to the device 8 andfor the device 8 are shown. The other device (not shown) and the device8 differ in the dimensions of the Hall bars. In the other device (notshown), the arms (not shown) are 4 μm wide and 80 μm long. In the device8 shown in FIGS. 2 a and 2 b, the arms 11 ₁, 11 ₂ are 1 μm wide and 20μm long.

These devices 8 exhibit in-plane magnetocrystalline anisotropy and havea saturation magnetisation, M_(s), of about 50 mT. This arises due tothe effect of strain relaxation rather than shape anisotropy. Forexample, shape anisotropy fields for the devices 8 are less than 1 mT,which is one order of magnitude lower than the magnetocrystallineanisotropy fields. Thus, the easy axes are not defined by shapeanisotropy, but rather than magnetocrystalline anisotropy.

A Curie temperature (T_(c)) of 100° K is estimated using Arrot plots ofanomalous Hall data. A hole density of 5×10²⁰ cm³ is estimated fromhigh-field Hall measurements. At this doping, compressive strain in theGa_(0.95)Mn_(0.05)As epilayer 13 grown on the GaAs substrate 15 producesa strong magnetocrystalline anisotropy which forces magnetization vectorto align parallel with the plane of the magnetic epilayer 13.

Magnetization orientations in the individual microbar devices 8 arelocally monitored by measuring longitudinal and transverse components ofthe anisotropic magnetoresistance (AMR) for in-plane rotating magneticfield (not shown).

FIGS. 3 a and 3 b illustrate magnetization rotation plots at saturationmagnetic field which show that the in-plane AMRs closely follow theform:

Δρ_(L) =A cos(2φ)   (2a)

Δρ_(T) =A sin(2φ)   (2b)

where ρ_(L) is longitudinal resistivity, ρ_(T) is transverseresistivity, A is a constant (not only for each Hall bar, but also forthe van der Pauw device 10) and φ is an angle between magnetization andcurrent. Δρ_(L,T)=ρ_(L,T)− ρ _(L,T) where ρ _(L,T) is the average overall angles.

FIGS. 3 c and 3 d show magnetoresistance plots for external magneticfield sweeps in which a field angle, θ, measured from the [1 10] axis,is constant.

As shown, magnetoresistance is strongly dependent at the values of θ andis attributed to magnetization rotations. At high fields, themagnetoresistance becomes purely isotropic, i.e. the differences betweenresistances for different angles θ become independent of the magnitudeof the external field. This property and the much smaller magnitude ofthe isotropic magnetoresistance compared to the low-field anisotropicmagnetoresistance enables the high-field measurements shown in FIGS. 3 aand 3 b to be used to determine a one-to-one correspondence between achange in the low-field resistance and a change in magnetizationorientation. The 45° phase shift between the longitudinal and transverseAMR traces shown in FIGS. 3 a and 3 b can be used to determine a changein the magnetization angle if both resistance components are measuredsimultaneously.

Fixed θ magnetoresistance measurements can used first to determine localmagnetic anisotropies in the individual microbars. Values of θcorresponding to easy-axis directions have the smallestmagnetoresistance. For values of θ not corresponding to easy axisdirections the magnetization undergoes a (partially) continuous rotationat low fields resulting in different orientations and, thus, differentmeasured resistances, at saturation and remanence. Using this technique,the easy-axis directions can be determined to within ±1°.

The effect of introducing spatial variation of strain on magneticanisotropy is shown in FIGS. 4 a and 4 b.

In bulk material, measured using the van der Pauw device 10 (FIG. 2 a),a magnetization angle 30° corresponds to an easy-axis, while 7° and 55°are significantly harder. However, in the device 8 shown in FIG. 2 a, 7°is an easy axes in the [1 10]-bar and 55° is an easy-axis in the[110]-bar.

Table 1 below lists easy axes found in the other device (not shown)labelled ‘A’, the device 8 labelled ‘B’ and in bulk material, i.e. inthe van der Pauw device 10:

TABLE 1 Sample Bulk A [1 10] A [110] B [1 10] B [110] Easy axis angle±30° ±15° ±36° +7°, −8° +55°, −63°

Bulk material has cubic anisotropy arising from the underlyingzincblende structure, plus an additional uniaxial [1 10] anisotropyarising from being an (Ga,Mn)As epilayer 13. This results in two easyaxes tilted by 15± from the [100] and [010] cube edges towards the [110] direction.

In the microdevices, i.e. the other device (not shown) and the device 8,the easy axes are rotated inwardly from the angles occupied in the bulkmaterial towards the arms 11 ₁, 11 ₂. The degree of rotation increasesas the width of the arms 11 ₁, 11 ₂ decreases.

The local changes in the magnetocrystalline anisotropy may be understoodin the following way.

Referring again to FIG. 2 a, Ga_(0.95)Mn_(0.05)As epilayers 13 grown onGaAs substrate are compressively strained in the (001) plane with thetypical value of the strain parameter:

$\begin{matrix}{f \equiv \frac{\left( {a_{GaMnAs} - a_{GaAs}} \right)}{a_{GaAs}}} & (3)\end{matrix}$

where a_(GaAs) and a_(GaMnAs) are the lattice parameters of cubic,fully-relaxed GaAs and (Ga,Mn)As, respectively. Using equation (3) aboveand values of a_(GaAs) and a_(GaMnAs), f≈0.2−0.3.

With (Ga,Mn)As material removed in the trenches 9 along the bars 11, thelattice can relax in a transverse direction and the correspondingextension can be roughly estimated as ft/w˜0.01, where t is thethickness of the (Ga,Mn)As film, in this case 25 nm, and w is the barwidth.

On a quantitative level, the strength of the lattice relaxation in themicrobars can be obtained using numerical elastic theory simulations forthe realistic sample geometry. GaAs values of the elastic constants areconsidered for the whole wafer including the Ga_(0.95)Mn_(0.05)Asepilayer 13.

Referring to FIG. 5, numerical simulations of strength of the latticerelaxation for the [1-10]-bar 11 ₂ of device 11 (FIG. 2 a) are shown.

FIG. 5 a shows the strain component along the growth-direction[001]-axis with respect to the lattice parameter of a fully relaxedcubic GaAs, namely:

e_([001])≡(a_([001])−a_(GaAs))/a_(GaAs)   (4)

Since strain components scale linearly with f, then e_([001])/f can beplotted.

FIG. 5 illustrates growth-induced lattice matching strain. Because ofin-plane compression of the (Ga,Mn)As lattice, the elastic medium reactsby expanding the lattice parameter in the growth direction, as comparedto a_(GaAs), i.e. e_([001])/f>1.

Within the plane of the epilayer 13 the lattice can relax only in adirection perpendicular to the microbar orientation. The correspondingstrain component, calculated again with respect to the GaAs, is plottedin FIG. 5 b over the entire cross-section of device 11 and in FIGS. 5 cand 5 d along various cross sections through the [001]-[110] plane.While in the centre of the bar the in-plane relaxation is relativelyweak, i.e. the lattice parameter remains similar to that of the GaAssubstrate 15, the lattice is strongly relaxed near the edges of the bar11. Averaged over the entire cross-section of the (Ga,Mn)As bar,relative in-plane lattice relaxation is found to be several hundredthsof a per cent, i.e. of the same order as estimated by the ft/wexpression. Microscopic magnetocrystalline energy calculations describedbelow confirm that these seemingly small lattice distortions can accountfor the observed easy-axis rotations in the strongly spin-orbit coupled(Ga,Mn)As.

Microscopic calculations of the magnetization angle dependent totalenergies are based on combining the six-band k.p description of the GaAshost valence band with kinetic-exchange model of the coupling to thelocal Mn_(Ga) d⁵-moments. The theory is well suited for the descriptionof spin-orbit coupling phenomena in the top of the valence band whosespectral composition and related symmetries are dominated, as in thefamiliar GaAs host, by the p-orbitals of the As sub-lattice. The k.pmodelling also provides straightforward means of accounting for theeffects of lattice strains on the (Ga,Mn)As band structure. As in theabove macroscopic simulations we assume that the elastic constants in(Ga,Mn)As have the same values as in GaAs. This theory, which uses noadjustable free parameters, has explained the observed transitionsbetween in-plane and out-of-plane easy magnetization orientations insimilar (Ga,Mn)As epilayers grown under compressive and tensile strainsand provided a consistent account of the signs and magnitudes ofcorresponding AMR effects.

For the modelling of the magnetocrystalline energy of the microbars,homogeneous strain in the (Ga,Mn)As layer corresponding to the averagevalue of e_([001]) obtained in the macroscopic simulations can beassumed. The input parameters of the microscopic calculations are straincomponents, related to the fully relaxed cubic (Ga,Mn)As lattice, in the└100┘-└010┘-└001┘ (x-y-z) coordinate system which are given by:

$\begin{matrix}\begin{matrix}{e_{ij} = \begin{pmatrix}e_{xx} & e_{xy} & 0 \\e_{yx} & e_{yy} & 0 \\0 & 0 & e_{zz}\end{pmatrix}} \\{= \begin{pmatrix}{{e_{\lbrack 110\rbrack}/2} - f} & {{\pm e_{\lbrack 110\rbrack}}/2} & 0 \\{{\pm e_{\lbrack 110\rbrack}}/2} & {{e_{\lbrack 110\rbrack}/2} - f} & 0 \\0 & 0 & {{e_{\lbrack 001\rbrack}/2} - f}\end{pmatrix}}\end{matrix} & (5)\end{matrix}$

where ± corresponds to the [1 10]-bar and [110]-bar respectively.

FIG. 6 a illustrates easy-axes orientations in the [1 10]- and[110]-bars of the other ‘L’-shaped device 15 and the L’-shaped device 8.Arrows 16 indicate the direction and strength of the patterning inducedlattice relaxation.

In FIG. 6 b, calculated magnetocrystalline energies are plotted as afunction of the in-plane magnetization angle for f=0.3 and e_(xy)ranging from zero (no in-plane lattice relaxation) to typical valuesexpected for the [1 10]-bar (e_(xy)>0) and for the [110]-bar (e_(xy)<0).In particular, energies are plotted for as a function of the in-planemagnetization angle for zero shear strain (black line), fore_(xy)=0.004, . . . , 0.02% corresponding to lattice extension along[110] axis and for e_(xy)=−0.004, . . . , −0.02% corresponding tolattice extension along [1 10] axis. The magnetic easy axes are ar ate_(xy)=0, 0.02% and −0.02%. Lattice deformations breaking the [110]-[110] symmetry of the microscopic magnetocrystalline energy profileare illustrated by the diamond-like unit cells extended along [110] axisfor the [110]-bar (bottom diamond) and along the [110]axis for the[110]-bar (right diamond).

Consistent with the experiment, the minima at [100] and [010] fore_(xy)=0 move towards the [1 10] direction for lattice expansion along[110] direction (e_(xy)>0) and towards the [110] direction for latticeexpansion along [1 10] direction (e_(xy)<0). The asymmetry betweenexperimental easy-axes rotations in the two bars is due to the [110]uniaxial component already present in bulk material whose microscopicorigin is not known, but can be modelled by an intrinsic (not induced bymicro-patterning) strain e_(xy) ^(bulk)˜+0.01%.

The devices just described use the mutual strain relaxation induced bymicro-patterning of stripes from GaMnAs with in-plane magneticanisotropy grown under compressive strain. On the other hand, wireswhich are patterned from tensile strained GaMnAs with perpendicularmagnetic anisotropy relax by reducing their lattice constant. In thiscase, micro-patterning weakens the perpendicular magnetic anisotropycompared to the tensile strained GaMnAs bulk layer.

Ferromagnetic metals also exhibit a sensitive dependence of themagnetocrystalline anisotropy on local strain. Any distortion of theequilibrium lattice changes the local anisotropy. In ultrathin films,strain is induced by the growth on a surface. Therefore, similar toGaMnAs, ultrathin layers of cobalt (Co), or iron (Fe) epitaxially grownon a GaAs [001] substrate exhibit both cubic magnetic anisotropy of thebulk, as well as a uniaxial contribution stemming from the interface.

Magnetic Anisotropy Due to Charge Carrier Density Variations

FIG. 7 shows magnetocrystalline energy profile of transverse strainedGa_(0.96)Mn_(0.04)As grown on GaAs [001] under compressive strain ofe₀=−0.2% with lattice deformation (expansion) along [1 10] ofe_(xy)=−0.02% for a first carrier density, p, of =8×10²⁰ cm⁻³ and asecond carrier density, p, of 6×10²⁰ cm⁻³. First and second arrows 17,18 indicate orientation of the easy axis for the first and secondcarrier densities respectively.

As shown in FIG. 7, changes in carrier density can yield variation ofthe magnetic anisotropy in strained GaMnAs. Although changing thecarrier-density in a highly doped (˜10²⁰-10²¹ cm⁻³) bulk semiconductormay be difficult to achieve due to a short screening length, significantcarrier density variations may be realized in sufficiently(electrically) isolated nanostructures.

Theoretical calculations similar to those presented in FIG. 6 b aboveindicate a sensitive dependence of the magnetic anisotropy on thecarrier density. As shown, FIG. 7, a reduction of ˜25% in carrierconcentration changes the easy axes by about 90° from ˜[1 10] to [110]crystallographic orientation.

Further embodiments of the invention will now be described which realizeelectric field induced variations of the magnetic anisotropy. Theseinclude changing the charge carrier density in a strained ferromagneticsemiconductor, shifting the centre of maximal carrier concentration inan inhomogenously strained ferromagnetic semiconductor system, andchanging strain in a ferromagnetic layer by attaching a piezoelectriclayer to the ferromagnetic layer or by exploiting piezoelectricproperties of the ferromagnetic material itself, as is possible in, forexample, GaMnAs (which has piezoelectric properties similar toconventionally doped GaAs).

Further Magnetoresistance Devices

Further embodiments of magnetoresistance devices in accordance with thepresent invention will now be described.

Firstly, magnetoresistance devices will be described in whichapplication of an electric field pulse causes a change in charge carrierdensity in a ferromagnetic region which in turn causes a change inmagnetic anisotropy which causes the magnetisation to begin precession.

Referring to FIGS. 8 a and 8 b, first and second magnetoresistivedevices 21 ₁, 21 ₂ are shown. The second devices 21 ₂ are variants ofthe first device 21 ₁.

Each device 21 ₁, 21 ₂ includes a ferromagnetic region 22 (herein alsoreferred to as a ferromagnetic “island”) which is under strain. In theseexamples, the ferromagnetic region 22 comprises a ferromagneticsemiconductor, such as (Ga,Mn)As. However, a different ferromagneticsemiconductor may be used.

The orientation of magnetisation of the ferromagnetic region 22 can bechanged or helped to change by applying a short electric field pulseusing a gate 23 capacitively coupled to the ferromagnetic region 22.Applying the electric field pulse causes a change in charge carrierdensity in the ferromagnetic region 22 which in turn causes a change inmagnetic anisotropy which causes the magnetisation to begin precession.The ferromagnetic region 22 may be sufficiently small that it exhibitscharging effects at a given operating temperature, such as at 4.2° K.For example, the ferromagnetic region 22 may have dimensions (layerthickness and lateral diameter) of the order of 1 or 10 nm. However, theferromagnetic region 22 may be larger, for example having dimensions ofthe order of 100 nm, 1 μm or higher.

The ferromagnetic island 22 is disposed between first and second leads24, 25, and is weakly coupled to the leads 24, 25 by respective tunnelbarriers 26, 27. In some embodiments, there may be more than one islandof ferromagnetic material, for example arranged in chain.

Reorientation of magnetisation is triggered using a pulse generator 28which applies a voltage pulse 29 to the gate 23.

Direction of orientation can be measured in different ways.

For example, in the first device 21 ₁, orientation of magnetisation canbe determined by measuring tunnelling anisotropic magnetoresistance(TAMR) using voltage source 30 and current detector 31. If the firstand/or second lead 24, 25 is ferromagnetic, then the orientation ofmagnetisation can be determined by measuring tunnellingmagnetoresistance (TMR) using voltage source 30 and current detector 31.In either case, the measurement involves applying a voltage so as todrive a current and measuring current.

In the second device 21 ₂, orientation of magnetisation can bedetermined using by measuring TMR using the voltage source 30 and thecurrent detector 31. However, the bias is applied across and current ismeasured between the first lead 24 and a third lead 32 which isconnected to a pinned ferromagnetic region 33 which is separated fromthe ferromagnetic island 22 by a tunnel barrier 34. It will beappreciated that a different measurement configuration can be used.

Referring to FIG. 9, the first device 21 ₁ is shown in more detail.

The first device 21 ₁ has an elongate conductive channel 36 with thegate 23 arranged to the side of the channel 36, i.e. in a side gateconfiguration. The channel 36 and side gate 23 are formed in a patternedlayer 37 of (Ga,Mn)As by trench-isolation. A layer 38 of AlAselectrically isolates the channel 36 and the side gate 23 from a GaAssubstrate 39. The channel 36 includes a constriction 40 disposed betweenwider portions which provide the leads 24, 25 to the constriction 40.

The (Ga,Mn)As layer 37 comprises 2% Mn, i.e. Ga_(0.98)Mn_(0.02)As, andhas a thickness of 5 nm, although the effective thickness may be about 3nm due to surface oxidation. The constriction 40 is 30 nm wide and 30 nmlong. The channel 36 is 2 μm wide. The channel 36 and the gate 23 areseparated by about 30 nm.

In the region of the constriction 40, potential fluctuations arisingfrom disorder create at least one conductive island 22 and at least apair of tunnel barriers 26, 27 which weakly couple the island 22 toleads 24, 25 and/or adjacent islands 22.

Referring to FIGS. 10 a to 10 c, characteristics of the first device 22₁ will be described.

FIG. 10 a is a greyscale plot of channel conductance against gatevoltage and in-plane parallel-to-current magnetic field. A dashed line41 highlights critical reorientation field, B_(C), which depends on gatebias. The critical reorientation field, B_(C), decreases from about 40mT at V_(G)=−1V to less than 20 mT at V_(G)=+1V.

Assuming a disk-shaped island 22, an effective disk diameter of about 10nm can be estimated using the experimentally-found value of chargingenergy. Thus, about 40 Manganese acceptors are present on the island 22.About sixteen Coulomb oscillations are observed if V_(G) is varied from−1V to +1V corresponding to a reduction of about 40% in carrier density.The critical reorientation field, B_(C), drops down from about 50 mT atV_(G)=−1V to less than 20 mT at V_(G)=+1V.

FIG. 10 b is plot of Coulomb blockade oscillations at B₀=0, where theisland 22 remains at a magnetization M₀, and at B₀=−100 mT, where theisland 22 remains at saturation magnetization M₁ over the gate voltagerange between V_(G)=−1 and 1V. Conductance measurements at anintermediate field B₀=−35 mT show a transition from M₀ to M₁ at acritical gate voltage of about −0.5V.

FIG. 10 c is a plot illustrating the dependence of criticalreorientation field, B_(C), against gate bias, V_(G), between V_(G)=−1Vand V_(G)=+1V. This indicates that a gate voltage pulse of amplitudeV_(G)≧2.5V can trigger magnetic switching at B₀=0. It will beappreciated that, if different device structure and/or materials a used,then a similar plot can obtained and used to find the bias required totrigger magnetic switching.

As shown in FIGS. 11 a and 11 b, the second device 21 ₂ is a variant ofthe first device 21 ₁.

The devices 21 ₂ may be formed growing a layer of AlAs 38′ on a GaAssubstrate 39 followed by a layer of (Ga,Mn)As (not shown), patterningthe (Ga,Mn)As to form a underlying electrode structure 42 comprising thepinned layer 32 and the third electrode 33 as a single piece, thengrowing a further layer of AlAs 43 and a further layer of (Ga,Mn)As overthe patterned substrate and patterning the further layer of (Ga,Mn)As toform the channel 37′ and gate 23.

An overlying electrode structure can be used instead of an underlyingelectrode structure. For example, the AlAs layer and (Ga,Mn)As layerforming the electrode may be grown after the channel and gate has beenformed and patterned to form the electrode structure comprising thepinned layer and the third electrode. Alternatively, a thin gatedielectric, such as Si_(x)N_(y), and a ferromagnetic material, such asCo may be deposited and patterned using lift-off or dry etching.

Referring to FIG. 12, writing and reading cycles for the first andsecond devices 21 ₁, 21 ₂ are shown.

As will be explained in more detail later, the devices 21 ₁, 21 ₂ canexhibit four states M₁, M₂, M₃, M₄. However, the devices 21 ₁, 21 ₂ canexhibit fewer states, for example just two states which may beanti-parallel, or more states, for example six states by takingadvantage of in-plane bi-axial anisotropy and perpendicular uni-axialanisotropy. Moreover, even if the devices 21 ₁, 21 ₂ can exhibit, forexample, four states M₁, M₂, M₃, M₄, depending on whether, for example,the source and/or drain region is ferromagnetic, all states may bedistinguishable or, alternatively, some states may be indistinguishable.

In the following, two types of write pulses will be described whichcauses magnetisation 44 of the ferromagnetic island 22, for one type ofpulse (so-called “t₁₈₀” pulse), to switch between two states and, foranother type of pulse (so-called “t₉₀” pulse), to switch between two“adjacent” states within four states.

It is noted that the plot of magnetisation 44 shown in FIG. 12 does notrepresent energy of magnetisation, but merely represents differentstates. In some embodiments, they may represent angle dependencies 0°,90°, 180°, 270°.

In the following, so-called “toggle” switching is described, wherebyapplying a “t₁₈₀” pulse 29 repeatedly causes magnetisation 44 to“toggle” between two states, e.g. M₁ and M₃ representing ‘0’ and ‘1’.However, a “t₉₀” pulse 29 repeatedly causes magnetisation 45 to “rotate”progressively from one state to a neighbouring state.

To write data to the device 21 ₁, 21 ₂, e.g. by switching between ‘0’and ‘1’ states and vice versa, a voltage pulse 29 is applied to the gate23.

The pulse 29 has duration, t₁₈₀, which is half the period of precession,t_(precess). The precession period, t_(precess), is given by:

$\begin{matrix}{t_{precess} = {{1/f_{precess}} = \frac{1}{\frac{\gamma}{2\pi}B_{A}}}} & (1)\end{matrix}$

where γ is the gyromagnetic constant γ=gμ_(B)/

(2.2×10¹⁵ mA⁻¹s⁻¹), B_(A) is the magnetic anisotropy field and mayinclude a demagnetising field, created by divergence in themagnetisation, e.g. at sample, grain, domain wall or other types ofboundaries, and causes shape anisotropy. In this example, t_(precess) isabout 1 ns. The value of t_(precess) may lie typically in the range of100 ps to 10 ns (for B_(a) 100 mT to 1 mT).

The magnitude of the voltage pulse, |V_(G)|, is of the order of 1 or 10V.

As explained earlier, an external magnetic field may be applied to helpstabilise magnetisation or to facilitate precession. The externalmagnetic field may be provided by a permanent magnet (not shown) or by aconductive track (not shown) and preferably has a magnitude which isabout the same order but smaller than the anisotropy field, for exampleof the order of 1 to 100 mT.

In some embodiments, an external magnetic field and/or spin transfertorque current may be used to write a particular state (as opposed totoggle between states) by orientating the magnetisation 44 in aparticular direction. Herein, this is referred to as “direct writing”.

In embodiments in which a magnetoresistance device has pinned and freeferromagnetic layers separated by an insulating layer, re-orientation ofthe magnetisation may achieved by applying the electric field pulse andsimultaneously or shortly afterwards applying a spin transfer torque(STT) current pulse. By “shortly afterwards”, we mean within a period oftime that magnetisation is still undergoing precession followingapplication of the electric field pulse and has not been damped.Typically, the period of time is between 0 and 5 ns.

To read data from the device 21 ₁, 21 ₂, a bias pulse 45 is appliedbetween the source 24 and drain 25 of the device 21 ₁, 21 ₂ and thecurrent 31, i, is measured. The magnitude of the current depends on thetunnelling anisotropic magnetoresistance (TAMR) and/or the tunnellingmagnetoresistance (TMR) of the device which in turn depends on theorientation of magnetisation 44 of the ferromagnetic region 22 whichrepresents ‘0’ and ‘1’ states.

As explained earlier, orientation of more than two states can bedetermined by measuring anisotropic magnetoresistance effects such asAMR, TAMR and CBAMR or by measuring a transverse Hall voltage betweenlead 32 and a reference (e.g. ground) arising from the anomalous Halleffect for states along a perpendicular-to plane magnetic easy axis.

Referring to FIGS. 13 a, 13 b and 13 c, fabrication of the first device21 ₁ will now be described.

Referring to FIGS. 13 a, the device 21 ₁ is fabricated from anultra-thin (5 nm) Ga_(0.98)Mn_(0.02)As epilayer 37″ grown along the[001] crystal axis on a AlAs 38″ buffer layer on a GaAs substrate 39 bylow-temperature molecular beam epitaxy (LT-MBE) and reference is made to“High-quality GaMnAs films grown with arsenic dimers” by R. P. Campion,K. W. Edmonds, L. X. Zhao, K. Y. Wang, C. T. Foxon, B. L. Gallagher andC. R. Staddon, Journal of Crystal Growth, volume 247, p 42 (2003).

Due to the high reactivity of the GaMnAs layer to alkaline developersused in optical lithography, Hall bar 14 is defined using electron-beamlithography using a poly-methyl-methacrylate (PMMA) resist developedusing ultrasound in a methyl isobutyl ketone/isopropanol 1:3 mixture at25° C.

Thermally-evaporated, high-electron-contrast Cr/Au registration marks(not shown) having thicknesses of 20 nm and 60 nm respectively arepatterned by lift-off using 1 μm-thick resist (not shown) and ˜250 nmelectron-beam diameter. A 30 s dip in 10% HCl solution is used prior toevaporation to assist adhesion of metal without unduly damaging theGaMnAs.

A ˜200 nm-thick layer of resist (not shown) is applied to the surface Sof the Ga_(0.98)Mn_(0.02)As epilayer 37. The finest features are definedusing an electron-beam (not shown) having a ˜15 nm beam diameter and ˜5pA current, with on-chip focusing at adjacent registration marks.Less-critical areas (not shown) are defined in the same resist by a ˜250nm beam at ˜1 nA. The high-resolution regions are arranged to be assmall as possible to minimise write time and pattern drift.

Referring to FIG. 13 b, the resist is developed to leave a patternedresist layer M as an etch mask.

Referring to FIG. 13 c, reactive-ion etching (RIE) is used for trenchisolation. Any RIE-related conductivity impairment is expected to beminimal compared with the high conductivity of the GaMnAs. The pressurein the RIE chamber (not shown) is 20 mTorr, with 20 sccm flow of bothSiCl₄ and Ar to provide the required mix of physical and chemical etchaction suitable for removing both GaAs and manganese.

A typical etch of 10-15 s at 100 W yielded a trench T having a depth of20-30 nm, safely through the GaMnAs layer.

Cr/Au (20 nm/300 nm) bond pads are thermally evaporated, again precededby an adhesion dip in HCl solution. The bond pads form a low-resistanceelectrical contact to the GaMnAs layer and no separate ohmicmetallisation is required.

In this example, devices are arranged in a Hall-bar layout aligned along[110] direction, with a 2 μm-wide channel and three pairs of Hall sensorterminals of 500 nm width at 10 μm intervals either side of theconstriction. However, other arrangements can be used.

The fabrication process hereinbefore described is modified to fabricatethe second devices 21 ₂.

A different initial layer structure is used having a thicker GaMnAslayer, e.g. 25 nm thick. The layer structure is patterned using electronbeam lithography and RIE to form an underlying electrode structure 44(FIG. 11 a). Then, another AlAs layer (having a thickness of 3 nm) and alayer of GaMnAs are grown by LT-MBE as described above. The structure ispatterned to define the channel in a similar way to the first device 21₁.

Techniques may be used to minimise contamination between patterning theunderlying electrode structure 44 (FIG. 11 a) and growing the AlAs andGaMnAs layers. For example, the underlying electrode structure 44 (FIG.11 a) may be patterned using ion-beam milling immediately after growthof the initial layer structure, then the additional layers grown withoutbreaking vacuum.

Referring to FIG. 8 c, a third magnetoresistive device 21 ₃ is shown.

The third device 21 ₃ is a two-terminal device having a ferromagneticregion 22 disposed between first and second leads 24, 25 and is weaklycoupled to one of the leads 24 by a tunnel barrier 26 and to the otherlead 25 by a tunable barrier 35 provided by a region of depletion formedby the semiconducting ferromagnetic region 22 and the lead 25.

In this example, the ferromagnetic region 22 comprises a p-typesemiconductor, e.g. Ga(Mn,As) and the lead 25 comprises an n-typesemiconductor, e.g. Si doped GaAs, and so the tunable barrier 35 is areversed-biases p-n junction. However, the lead may be metallic and sothe tunable barrier 35 may be a Schottky barrier.

Referring in particular to FIGS. 14 a and 14 b, the third device 21 ₃ isshown in more detail.

The device 21 ₃ comprises a pillar 47 upstanding from a substrate 48.The pillar 47 includes a layer 25 of GaAs doped to a concentration ofthe order of 1-10×10¹⁸ cm³ and having an (unetched) thickness of 200 nm,a layer 22 of p-type Ga_(0.98)Mn_(0.02)As having a thickness of about 5nm, a layer 26 of AlAs having a thickness of 25 nm and a layer of Auhaving a thickness of about 10 nm.

The device is fabricated from a layer structure (not shown) grown on anGaAs substrate (not shown) comprising, in order a 200 nm thick layer ofn-type GaAs (not shown), a 5 nm thick layer of Ga_(0.98)Mn_(0.02)As anda 25 nm thick layer of AlAs. The Ga_(0.98)Mn_(0.02)As is grown bylow-temperature molecular beam epitaxy (LT-MBE).

Electron beam lithography and thermal evaporation are used to define apad of gold (Au) having a thickness of the order of 10 nm on the surfaceof the layer structure (not shown) and SiCl₄/Ar RIE is used to definethe pillar 47.

To contact the top of the pillar 47, the pillar may be planarised using,for example polyimide, and depositing a gold contact pad.

A non-magnetic ohmic contact is used to contact the substrate.

Referring to FIG. 14, writing and reading cycles for the third devices21 ₃ are shown.

Similar to the first and second devices 21 ₁, 21 ₂ described earlier,the third device 21 ₃ can exhibit can exhibit four states M₁, M₂, M₃,M₄.

The third device 21 ₃ differs in that the polarity of a voltage pulse 29determines whether it is a write or read pulse.

To write data to the device 21 ₃, a negative voltage pulse 29 is appliedto the lead 24 adjacent to the fixed tunnel barrier relative to theother lead 25 so as to reverse bias the p-n junction 35 and increase thewidth of the depletion region to increase depletion and vary the carrierdensity or carrier density distribution in the ferromagnetic region 22and, thus, induce precession. As explained earlier, the duration of thepulse can be use to switch between two states or between more than twostates, in other words using t₉₀ and t₁₈₀ pulses.

To read data, a positive bias pulse 30 is applied to the lead 24adjacent to the fixed tunnel barrier relative to the other lead 25 andthe magnetization orientation depending current 46, i, is measured.

Referring to FIGS. 16 a, 16 b and 16 c, a magnetoresistive device 51will now be described in which application of an electric field pulsecauses a shift in maximal carrier concentration in an inhomogeneouslystrained ferromagnetic semiconductor which in turn causes a change inmagnetic anisotropy and so initiates precession of magnetisation.

The device 51 comprises a Hall bar 52 which is generally elongate havingwidth, w, of about 1 μm and a length, l, of about 20 μm. The Hall bar 52has first and second end leads 53, 54 and first, second, third andfourth side leads 55, 56, 57, 58 arranged in pairs on opposite sides ofthe bar 52. The Hall bar 52 is sandwiched between underlying andoverlying electrodes 59, 60, hereinafter referred to as “bottom” and“top” electrodes respectively.

As shown, a pulse generator 61 is used to apply a voltage pulse 62between the top and bottom electrodes 59, 60. A current source 63 isused to apply a read current, i_(read), through the Hall bar 52 betweenthe first and second end leads 53, 54. First and second voltage meters64, 65 measure bias between the first and second leads 55, 56 andbetween the second and fourth side leads 56, 58 so as to determinelongitudinal and transverse anisotropic magnetoresistance (AMR)respectively. The bias measured between the second and third side leads56, 57 can also be used to measure the anomalous Hall effect (AHE)resistance.

An AMR measurement can be used to distinguish between two states wheremagnetization rotates by less than 180°, e.g. 90°, in a ferromagneticlayer exhibiting biaxial, in-plane anisotropy at V_(G)=V₀, for exampleV₀=0.

An AHE measurement can be used to distinguish between up and down statesin a system with perpendicular anisotropy at V_(G)=V₀.

Referring in particular to FIGS. 16 b and 16 c, the Hall bar 52 isformed on an indium gallium arsenide (In_(0.05)Ga_(0.95)As) substrate 66which serves as the bottom electrode 59. The Hall bar 52 includes a basebarrier layer 67 formed of AlAs overlying the InGaAs substrate 66, aninhomogeneously-strained ferromagnetic layer 68 formed of gradedInGaMnAs and a top barrier layer 69 formed of AlAs. The top gateelectrode 60 is formed of Al.

The lattice constant within the ferromagnetic layer 68 is controllablyvaried so as to produce inhomogeneous strain within the layer 68. Thelattice constant of In_(0.03)Ga_(0.97)As is larger than the latticeconstant for Ga_(0.95)Mn_(0.05)As so that the subsequentGa_(0.95)Mn_(0.05)As grown on In_(0.03)Ga_(0.97)As is tensile strained.Further on, Indium is introduced again to form InGaMnAs. The Indiumconcentration is increased until the lattice constant of InGaMnAsbecomes larger than the lattice constant of the InGaAs substrate toachieve compressive strain.

The device 51 is fabricated from a wafer 70 comprising an indium galliumarsenide (In_(y)Ga_(1-y)As) substrate 66′ (y=5%), a layer of aluminiumarsenide (AlAs) 67′ having a thickness of ˜20 nm, a graded layer ofindium gallium manganese arsenide (In_(z)Ga_(1-x-z)Mn_(x)As) 68′, whichincludes a base layer of GaMnAs 68 ₁′, and which has a thickness of ˜10nm.

Referring to FIG. 17, a layer 68 ₁′ of Ga_(1-x)Mn_(x)As is epitaxiallygrown under tensile strain on top of the AlAs layer 67′ which in turn isgrown on the In_(y)Ga_(1-y)As substrate 66′. In this example, theconcentration of manganese is 5%, i.e. x=0.05 and the concentration ofindium increases from z=0 to 10%.

The wider lattice constant of the In_(y)Ga_(1-y)As substrate 66′ istransmitted to the Ga_(1-x)Mn_(x)As layer 68 ₁′ which introduces tensilestrain. During further growth of the In_(z)Ga_(1-x-z)Mn_(x)As 68′,indium is introduced to increase further the lattice constant by therebyforming a quaternary alloy, InGaMnAs. The indium concentration └In┘increases with increasing distance, d, from the base 71 of the layer 68₁.

Different strain profiles can be used. For example, instead of thestrain within the ferromagnetic layer 68 varying from being tensilecloser to the substrate to being compressive further away from thesubstrate, it may change from being compressive to tensile. This can beachieved by fabricating the device from a wafer having a galliumarsenide (GaAs) substrate instead of In_(y)Ga_(1-y)As substrate andintroducing phosphorous (P) instead of indium (In) to form a gradedlayer of gallium manganese phosphide arsenide(Ga_(1-x)Mn_(x)P_(z)As_(1-z)). The lattice constant is reduced as thephosphorous concentration is increased.

Referring to FIG. 18, strain can also be varied by changing the shape offerromagnetic layer 68. For example, the width of the ferromagneticlayer 68 may be made narrower at the base 71 of the layer 68 having awidth w₁ and made wider further away from the base 71 having a widthw₂>w₁. Thus, the lattice is more relaxed in the thinner, lower part ofthe layer 68 than in the thicker, upper part of the layer 68. Theferromagnetic layer 68 may be homogenously doped.

Referring to FIG. 19 and 19 a, by applying a gate pulse 62 between thetwo gates 59, 60, an electric field 72 is generated which shifts chargecarriers 73 (here only holes, the majority carriers, are illustrated)and alters charge carrier concentration in a lower, tensile-strainedregion 74 and in an upper, compressively-strained region 75. Inparticular, the pulse draws carriers 73 from the lower, tensile-strainedregion 74 into the upper, compressively-strained region 75 so as toincrease charge carrier density in the upper, compressively-strainedregion 75.

Table 2 below identifies orientation of magnetic anisotropy with strainand carrier concentration:

TABLE 2 Tensile Strain Compressive strain High carrier concentration Outof plane In plane Low carrier concentration In plane Out of plane

Magnetic anisotropy 76 of the magnetic layer 68 changes from beingorientated in a first position 77 ₁ perpendicular to the plane of thelayer 68 (i.e. along axis 78) to a second orientation 77 ₂ orientatedalong the plane of the layer 68 (e.g. along axis 79). Thus, theeffective anisotropy field B_(A) rotates by 90°. This causes themagnetisation 80 to begin precession and to be re-orientated by 90degree for a π/2-pulse.

As will be explained in more detail later, application of another,identical pulse 62 causes the effective anisotropy field B_(A) to rotateagain by 90° so that the magnetization continues precession by another90°. Thus, the effective anisotropy field B_(A) becomes again orientatedalong the out-of-plane axis 77, but the magnetization goes in a thirdorientation 77 ₃ which is anti-parallel to the first orientation 77 ₁.Notwithstanding this, the magnetoresistance of the first and thirdstates (i.e. when the magnetisation 80 is aligned in these first andthird orientations 77 ₁, 77 ₃) is the same. This is because, asexplained earlier, an AMR measurement can distinguish between initialand final magnetization states only if they are not co-linear. An AHEmeasurement can distinguish between the two opposite magnetizationorientations perpendicular-to-plane. A TMR measurement can distinguishbetween parallel and antiparallel orientation with respect to a fixedreference layer.

Writing and reading cycles are similar to those shown in FIG. 12described earlier. However, during a read cycle, instead of applying asource-drain bias and measuring current, a current is driven through thedevice and the potential difference developed between leads 55, 56, 57,58 is measured.

The device 51 is fabricated using similar techniques to those describedearlier to fabricate the first device 21 ₁. For example, a layerstructure is grown in a similar way to that described earlier and ispatterned using electron-beam lithography and RIE.

Referring to FIGS. 20 a and 20 b, a fourth magnetoresistive device 81will now be described in which application of a strain pulse causes achange in magnetic anisotropy and so starts precession of magnetisation.

The device 81 comprises a stacked layer structure 82 mounted on apiezoelectric layer 83 having first and second contact leads 84, 85.First and second contacts 86, 87 are used to provide electrical contactsto the layer structure 82.

The stacked layer structure 82 has a width, W, of about 1 μm and alength, L, of about 1 μm.

As shown, a pulse generator 88 is used to apply a voltage pulse 89between the piezoelectric contact leads 86, 87. A voltage source 90 isused to apply a bias between the contact 86, 87 and a current meter 91is used to measure the current flowing through the stacked layerstructure 82.

Referring in particular to FIG. 20 b, the stacked layer structure 82 isformed on a gallium arsenide (GaAs) substrate 92 which mounted by glue93 to the piezoelectric stressor 83. The piezoelectric stressor isformed from lead-zirconate-titanate (PZT).

The stacked layer structure 82 includes a bottom contact layer 94comprising (non-ferromagnetic) n⁺-GaAs, a ferromagnetic layer 95 havinga relatively low coercivity (i.e. a “free” layer) comprisingGa_(0.98)Mn_(0.02)As and having a thickness of 5 nm, a tunnel barrierlayer 96 comprising aluminium arsenide (AlAs) having a thickness of 25nm, a ferromagnetic layer 97 having a relatively high coercivity (i.e. a“pinned” layer) comprising Ga_(0.98)Mn_(0.02)As having a thickness of 50nm and a top contact layer 98 comprising (non-ferromagnetic) gold.

Other arrangements and other materials may be used. For example, thepiezoelectric stressor 83 may be integrally formed with the substrate92. For example, GaAs is piezoelectric along the [110] axis.

It will be appreciated that the ferromagnetic layer(s) of the fourthdevice 81 need not be a semiconductor but may be metallic and maycomprise a material, such as ferromagnetic metals like Fe, Ni, Co ormetal alloys FePt, CoPt, CoPd or another suitable transition metal/noblemetal alloy.

Writing and reading cycles are similar to those shown in FIG. 13described earlier.

A stacked layer structure need not be used. Instead, an “in-plane”transport structure, e.g. similar to that shown in FIG. 9, can be used.For example, the structure shown in FIG. 9 may be mounted on apiezoelectric stressor 83.

Referring to FIGS. 21 a and 21 b, a fifth magnetoresistive device 101will now be described in which application of strain together with anelectric pulse causes a change in magnetic anisotropy and so startsprecession of magnetisation.

The device 101 comprises a cruciform mesa 102 which defines a channel103 of ferromagnetic material, which in this case is a delta-doped layerof Ga_(0.98)Mn_(0.02)As embedded in layer 104 of GaAs, and which issupported by substrate 105. First, second, third and fourth contact 106,107, 108, 109 provide contacts to the distal ends of the channel 103 anda surface top gate 110 is used to control magnetic anisotropy. Thesubstrate 104 is mounted on a piezoelectric layer 111 having first andsecond contacts 112, 113 which are used to generate an electric fieldwithin the piezoelectric layer 111 for pre-stressing the ferromagneticchannel 103.

The arms of the channel 103 each have a width of about 2 μm and a lengthof about 20 μm.

As shown, a first pulse generator 114 is used to apply a voltage pulse115 between the piezoelectric contact leads 112, 113 for pre-stressingthe channel 103. A second pulse generator 116 is used to apply a voltagepulse 117 to the surface gate 110 for inducing precession of magneticanisotropy.

A voltage source 118 is used to apply a bias 119 between the first andsecond contact 106, 107 and a current meter 120 is used to measure thecurrent 121 flowing between the third and fourth contacts 108, 109.

Referring in particular to FIG. 20 b, the substrate 104 is mounted tothe piezoelectric layer 111 by a layer of glue 122.

Writing and reading cycles are similar to those shown in FIG. 12described earlier. However, as shown in FIG. 22, a voltage pulse 115 isapplied and during the t₁₈₀ or t₉₀ pulse.

In the embodiments hereinbefore described, writing and reading of datato the devices is based on treating the device as if it had only twostates and, thus, store only one bit of information per device. However,taking advantage of biaxial in-plane anisotropy and uniaxialperpendicular-to-plane anisotropy, six remnant magnetisationorientations can be accessed using two types of combination of pulsesand inverted pulses so as to encode more than 2 bits (i.e. In 6/ln 2≈2.6corresponding to 6 different states).

Referring to FIG. 23, the ferromagnetic layers 22, 68, 95, 103 exhibitsix remnant magnetisation orientations 131, 132, 133, 134, 135, 136.

The ferromagnetic layers 22, 68, 95, 103 can be operated in two regimes,namely a biaxial in-plane anisotropy regime in which two types of biaspulse are applied relative to a zero dc bias offset (i.e. V_(G)=V₀) anda perpendicular anisotropy regime in which an inverted bias pulse isapplied, i.e. a bias pulse is applied relative to non-zero dc biasoffset (i.e. V_(G)=V_(C)).

At V_(G)=V₀, precessional switching triggered by fast gate-voltagepulses with different pulse lengths rotate the magnetization vectorbetween the four remnant states 131, 132, 133, 134 along the two biaxialeasy axes within the layer plane.

Referring to FIG. 24, in one sense, an adjacent magnetisationorientation 131, 132, 133, 134 can be accessed from another of thefirst, second, third and fourth magnetisation orientations 131, 132,133, 134 using a gate pulse 29, 62, 91 which effects a 90° rotation.This type of pulse is herein referred to as a “p^(90°) pulse” or “t₉₀pulse”.

In an opposite sense, an adjacent magnetisation orientation 131, 132,133, 134 can be accessed from another of the first, second, third andfourth magnetisation orientations 131, 132, 133, 134 using a gate pulse(not shown) which effects a 270° rotation. These pulses are hereinafterreferred to as a “p^(270°) pulse” or “t₂₇₀ pulse”.

The first, second, third and fourth magnetisation orientations 131, 132,133, 134 can also be accessed from a co-linear orientations 131, 132,133, 134 using a gate pulse 138 which effects a 180° rotation,hereinafter referred to as a “p^(180°) pulse” or “t₁₈₀ pulse”. Thus, thefirst magnetisation orientation 131 can be access the thirdmagnetisation orientation 133 using the p^(180°) pulse 138.

Changing between biaxial-in-plane and uniaxial-perpendicular-to-planeanisotropy regimes is achieved by “adiabatic” magnetizationreorientation which exploits dissipative damping. For example, after agate bias has changed from V₀ to V_(C), the magnetization vector Mstarts precessing around a modified anisotropy field B_(A)(V_(C)) anddissipative damping causes the magnetization vector to spiral towardsmodified anisotropy field B_(A)(V_(C)). The magnetization vector Meventually aligns (within thermal fluctuations) along one of the easyaxes corresponding to the modified anisotropy.

Regime changes are achieved by gate bias step changes 139, 140 which arehereinafter referred to as a “p^(damping) pulse” and an “invertedp^(damping) pulse” respectively.

The fifth and sixth magnetisation orientations 135, 136 can be accessedby using a gate pulse 141 which effects a 180° rotation. However, thepulse 141 is inverted with respect to the p^(180°) pulse 108 and ishereinafter referred to as an “inverted p^(180°) pulse.

Referring to FIGS. 25 a and 25 b, the effect of applying a p^(90°) pulse137 and an inverted p^(180°) pulse 141 are shown.

FIGS. 25 a illustrates precessional 90° switching in the biaxialin-plane anisotropic regime at V_(G)=V₀. As shown, the magneticanisotropy changes from being in-plane to beingperpendicular-to-the-plane during the gate voltage pulse 137 atV_(G)=V_(C) and switches back to V₀ after the magnetization vector M hasfinished the 90° rotation.

FIGS. 25 b shows that an inverted pulse triggers a 180° reversal in theperpendicular-to-plane anisotropy regime.

An AHE measurement can distinguish between two uniaxial magnetizationstates along perpendicular-to-the-plane orientation and measurements oftransverse and longitudinal AMR can unambiguously distinguish the 4biaxial magnetization states within the plane.

It will be appreciated that many modifications may be made to theembodiments hereinbefore described. For example, the ferromagnetic layermay have a different thickness, for example between 5 and 20 nm. Devicesmay operate based on electron or hole transfer. A capping layer may beused to protect the GaMnAs layer. The magnetoresistive device can have amultiple layer structure, such as a magnetic tunnel junction or spinvalve.

1. A method of operating a magnetoresistive device comprising aferromagnetic region configured to exhibit magnetic anisotropy and toallow magnetisation thereof to be switched between at least first andsecond orientations and a gate capacitively coupled to the ferromagneticregion, the method comprising: applying an electric field pulse to theferromagnetic region so as to cause orientation of magnetic anisotropyto change for switching magnetisation between the first and secondorientations.
 2. A method according to claim 1, comprising: exclusivelyapplying the electric field pulse to the ferromagnetic region so as tocause magnetisation of the ferromagnetic region to switch between thefirst and second orientations.
 3. A method according to claim 1,comprising: arranging for magnetisation of the ferromagnetic region toswitch between the first and second orientations without applying amagnetic field pulse.
 4. A method according to claim 1, wherein thedevice further comprises a conductive path running adjacent to theferromagnetic region for generating a magnetic field pulse, the methodfurther comprising: applying a magnetic field pulse to the ferromagneticregion while applying the electric field pulse so to enhance the changein orientation of an effective magnetic field comprising anisotropyfield and applied magnetic field so as to switch the magnetisationbetween the first and second orientations.
 5. A method according toclaim 4, comprising: applying a leading edge of the electric field pulsebefore applying a leading edge of the magnetic field pulse.
 6. A methodaccording to claim 1, wherein the device further comprise anotherferromagnetic region having a higher coercivity than the ferromagneticlayer and separated therefrom by a tunnel barrier layer, the methodfurther comprising: applying a spin transfer current pulse passingthrough ferromagnetic regions while applying the electric field pulse soas to switch the magnetisation between the first and secondorientations.
 7. A method according to claim 6, comprising: applying aleading edge of the electric field pulse before applying a leading edgeof the spin transfer current pulse.
 8. A method according to claim 1,wherein the ferromagnetic region comprises a ferromagnetic semiconductorhaving an inhomogeneous strain distribution and the method comprises:applying an electric field pulse of sufficient magnitude to varydistribution of charge carriers relative to the inhomogeneous straindistribution.
 9. A method according to claim 8, wherein theinhomogeneous strain distribution comprises a region of compressivestrain and a region of tensile strain.
 10. A method according to claim8, wherein the ferromagnetic semiconductor comprises (Ga,Mn)As.
 11. Amethod according to claim 1, comprising: applying an electric fieldpulse having a duration, t, which is a multiple of a quarter oft_(precess) about:$t_{precess} = {{1/f_{precess}} = \frac{1}{\frac{\gamma}{2\pi}B_{A}}}$where γ is the gyromagnetic constant γ=gμ_(B)/

(2.2×10¹⁵ mA⁻¹s⁻¹) and B_(A) is the magnetic anisotropy field of theferromagnetic semiconductor.
 12. A method according to claim 11,comprising applying a pulse having a duration, t, between 0 and 5 ns.13. A method according to claim 1, further comprising: applying amagnetic field to the ferromagnetic region independently of applying theelectric field pulse so as to assist switching of the magnetisation ofthe ferromagnetic region between the first and second orientations. 14.A method according to claim 1, further comprising: applying stress tothe ferromagnetic region and, while the stress is applied, applying theelectric field pulse.
 15. A method of operating a magnetoresistivedevice comprising a ferromagnetic region configured to exhibit magneticanisotropy and to allow magnetisation thereof to be switched between atleast first and second orientations, the method comprising: applying astress pulse to the ferromagnetic region so as to cause orientation ofmagnetic anisotropy to change for switching magnetisation between thefirst and second orientations.
 16. A method according to claim 15,wherein the device comprises a piezoelectric region mechanically coupledto the ferromagnetic region and wherein applying the stress pulsecomprises applying a voltage pulse across the piezoelectric region. 17.A method according to claim 15, further comprising: applying an electricfield pulse to the ferromagnetic region while the stress pulse isapplied to the ferromagnetic region.
 18. Apparatus comprising:magnetoresistance device comprising a ferromagnetic region configured toexhibit magnetic anisotropy and to allow magnetisation thereof to beswitched between at least first and second orientations; and circuitryconfigured to operate the device according to any preceding claim.
 19. Amagnetoresistive device comprising: a ferromagnetic region configured toexhibit magnetic anisotropy and to allow magnetisation thereof to beswitched between at least first and second orientations; means forapplying stress to the ferromagnetic region in response to a firstelectrical input; and means for applying an electric field to theferromagnetic region in response to a second electrical input.
 20. Amagnetoresistive device according to claim 19, wherein means forapplying stress comprises a piezoelectric region coupled to theferromagnetic region and the means for applying an electric fieldcomprises at least one gate electrode.